Korpelevich's method for variational inequality problems on Hadamard manifolds

摘要

The concept of pseudomonotone vector field on Hadamard manifold is introduced. A variant of Korpelevich's method for solving the variational inequality problem is extended from Euclidean spaces to constant curvature Hadamard manifolds. Under a pseudo-monotone assumption on the underlying vector field, we prove that the sequence generated by the method converges to a solution of variational inequality, whenever it exists. Moreover, we give an example to show the effectiveness of our method.